C*-algebras generated by radial Toeplitz operators on polyanalytic weighted Bergman spaces
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , , |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916570190577664 |
|---|---|
| author | Barrera-Castelán, Roberto Moisés Maximenko, Egor A. Ramos-Vazquez, Gerardo |
| author_facet | Barrera-Castelán, Roberto Moisés Maximenko, Egor A. Ramos-Vazquez, Gerardo |
| contents | In a previous paper (Radial operators on polyanalytic weighted Bergman spaces, Bol. Soc. Mat. Mex. 27, 43), using disk polynomials as an orthonormal basis in the $n$-analytic weighted Bergman space, we showed that for every bounded radial generating symbol $a$, the associated Toeplitz operator, acting in this space, can be identified with a matrix sequence $γ(a)$, where the entries of the matrices are certain integrals involving $a$ and Jacobi polynomials. In this paper, we suppose that the generating symbols $a$ have finite limits on the boundary and prove that the C*-algebra generated by the corresponding matrix sequences $γ(a)$ is the C*-algebra of all matrix sequences having scalar limits at infinity. We use Kaplansky's noncommutative analog of the Stone--Weierstrass theorem and some ideas from several papers by Loaiza, Lozano, Ramírez-Ortega, Ramírez-Mora, and Sánchez-Nungaray. We also prove that for $n\ge 2$, the closure of the set of matrix sequences $γ(a)$ is not equal to the generated C*-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_06231 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | C*-algebras generated by radial Toeplitz operators on polyanalytic weighted Bergman spaces Barrera-Castelán, Roberto Moisés Maximenko, Egor A. Ramos-Vazquez, Gerardo Operator Algebras Functional Analysis 47L80, 47B35, 22D25, 30H20, 30G20, 33C45 In a previous paper (Radial operators on polyanalytic weighted Bergman spaces, Bol. Soc. Mat. Mex. 27, 43), using disk polynomials as an orthonormal basis in the $n$-analytic weighted Bergman space, we showed that for every bounded radial generating symbol $a$, the associated Toeplitz operator, acting in this space, can be identified with a matrix sequence $γ(a)$, where the entries of the matrices are certain integrals involving $a$ and Jacobi polynomials. In this paper, we suppose that the generating symbols $a$ have finite limits on the boundary and prove that the C*-algebra generated by the corresponding matrix sequences $γ(a)$ is the C*-algebra of all matrix sequences having scalar limits at infinity. We use Kaplansky's noncommutative analog of the Stone--Weierstrass theorem and some ideas from several papers by Loaiza, Lozano, Ramírez-Ortega, Ramírez-Mora, and Sánchez-Nungaray. We also prove that for $n\ge 2$, the closure of the set of matrix sequences $γ(a)$ is not equal to the generated C*-algebra. |
| title | C*-algebras generated by radial Toeplitz operators on polyanalytic weighted Bergman spaces |
| topic | Operator Algebras Functional Analysis 47L80, 47B35, 22D25, 30H20, 30G20, 33C45 |
| url | https://arxiv.org/abs/2306.06231 |